I was thinking of using convex function properties to prove the following inequality but couldn't. I'm not sure what else should I use. $\displaystyle 1-(a/b)<ln(b/a)<(b/a) -1 $ given that $\displaystyle 0<a<b$
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Originally Posted by GIPC $\displaystyle 1-(a/b)<ln(b/a)<(b/a) -1 $ given that $\displaystyle 0<a<b$ Use the mean value theorem to prove Napier's inequality: $\displaystyle \frac{1}{b}\le\frac{\log(b)-\log(a)}{b-a}\le\frac{1}{a}$.
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